Shortest distance between two skew lines using scalar triple product for JEE

Formula

\(d=\frac{|(\vec a_2-\vec a_1)\cdot(\vec b_1\times\vec b_2)|}{|\vec b_1\times\vec b_2|}\)

Variables: Lines are \(\vec r=\vec a_1+\lambda\vec b_1\) and \(\vec r=\vec a_2+\mu\vec b_2\).

Conditions: Applicable for non-parallel lines, so \(\vec b_1\times\vec b_2\neq \vec 0\).

Standard JEE formula for shortest distance between skew lines.